The physics
A charged capacitor joined to a coil pushes a current through it. The coil fights any change in its current. So the charge swings back and forth, like a mass on a spring.
q = q₀ cos ωt i = q₀ ω sin ωt ω = 1/√(LC)
With no resistance, the total energy stays the same. It moves from the capacitor to the coil and back. When the capacitor is empty, the coil holds it all. Then the current is largest.
q²/2C + ½ L i² = q₀²/2C T = 2π√(LC)
The capacitor first empties after a quarter period. The coil's share of the energy is sin²ωt. So it does not grow at a steady rate.
A steady emf ε in the loop makes the charge swing about Cε. It goes from 0 to 2Cε and back.